Evolution of localized blobs of swirling or buoyant fluid with and without an ambient magnetic field.

We investigate the evolution of localized blobs of swirling or buoyant fluid in an infinite, inviscid, electrically conducting fluid. We consider the three cases of a strong imposed magnetic field, a weak imposed magnetic field, and no magnetic field. For a swirling blob in the absence of a magnetic field, we find, in line with others, that the blob bursts radially outward under the action of the centrifugal force, forming a thin annular vortex sheet. A simple model of this process predicts that the vortex sheet thins exponentially fast and that it moves radially outward with constant velocity. These predictions are verified by high-resolution numerical simulations. When an intense magnetic field is applied, this phenomenon is suppressed, with the energy and angular momentum of the blob now diffusing axially along the magnetic field lines, converting the blob into a columnar structure. For modest or weak magnetic fields, there are elements of both types of behavior, with the radial bursting dominating over axial diffusion for weak fields. However, even when the magnetic field is very weak, the flow structure is quite distinct to that of the nonmagnetic case. In particular, a small but finite magnetic field places a lower bound on the thickness of the annular vortex sheet and produces an annulus of counter-rotating fluid that surrounds the vortex core. The behavior of the buoyant blob is similar. In the absence of a magnetic field, it rapidly develops the mushroomlike shape of a thermal, with a thin vortex sheet at the top and sides of the mushroom. Again, a simple model of this process predicts that the vortex sheet at the top of the thermal thins exponentially fast and rises with constant velocity. These predictions are consistent with earlier numerical simulations. Curiously, however, it is shown that the net vertical momentum associated with the blob increases linearly in time, despite the fact that the vertical velocity at the front of the thermal is constant. As with the swirling blob, an imposed magnetic field inhibits the formation of a vortex sheet. A strong magnetic field completely suppresses the phenomenon, replacing it with an axial diffusion of momentum, while a weak magnetic field allows the sheet to form, but places a lower bound on its thickness. The magnetic field does not, however, change the net vertical momentum of the blob, which always increases linearly with time.

The effect of shape on the adhesion of fibrillar surfaces.

Experimental data have demonstrated that mushroom-shaped fibrils adhere much better to smooth substrates than punch-shaped fibrils. We present a model that suggests that detachment processes for such fibrils are controlled by defects in the contact area that are confined to its outer edge. Stress analysis of the adhered fibril, carried out for both punch and mushroom shapes with and without friction, suggests that defects near the edge of the adhesion area are much more damaging to the pull-off strength in the case of the punch than for the mushroom. The simulations show that the punch has a higher driving force for extension of small edge defects compared with the mushroom adhesion. The ratio of the pull-off force for the mushroom to that of the punch can be predicted from these simulations to be much greater than 20 in the friction-free case, similar to the experimental value. In the case of sticking friction, a ratio of 14 can be deduced. Our analysis also offers a possible explanation for the evolution of asymmetric mushroom shapes (spatulae) in the adhesion organ of geckos.

Encoding of mixtures in a simple olfactory system.

Natural odors are usually mixtures; yet, humans and animals can experience them as unitary percepts. Olfaction also enables stimulus categorization and generalization. We studied how these computations are performed with the responses of 168 locust antennal lobe projection neurons (PNs) to varying mixtures of two monomolecular odors, and of 174 PNs and 209 mushroom body Kenyon cells (KCs) to mixtures of up to eight monomolecular odors. Single-PN responses showed strong hypoadditivity and population trajectories clustered by odor concentration and mixture similarity. KC responses were much sparser on average than those of PNs and often signaled the presence of single components in mixtures. Linear classifiers could read out the responses of both populations in single time bins to perform odor identification, categorization, and generalization. Our results suggest that odor representations in the mushroom body may result from competing optimization constraints to facilitate memorization (sparseness) while enabling identification, classification, and generalization.

Encoding of mixtures in a simple olfactory system

Natural odors are usually mixtures; yet, humans and animals can experience them as unitary percepts. Olfaction also enables stimulus categorization and generalization. We studied how these computations are performed with the responses of 168 locust antennal lobe projection neurons (PNs) to varying mixtures of two monomolecular odors, and of 174 PNs and 209 mushroom body Kenyon cells (KCs) to mixtures of up to eight monomolecular odors. Single-PN responses showed strong hypoadditivity and population trajectories clustered by odor concentration and mixture similarity. KC responses were much sparser on average than those of PNs and often signaled the presence of single components in mixtures. Linear classifiers could read out the responses of both populations in single time bins to perform odor identification, categorization, and generalization. Our results suggest that odor representations in the mushroom body may result from competing optimization constraints to facilitate memorization (sparseness) while enabling identification, classification, and generalization